This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.
Metamath Proof Explorer
Description: Theorem *4.37 of WhiteheadRussell p. 118. (Contributed by NM, 3-Jan-2005)
|
|
Ref |
Expression |
|
Assertion |
orbi1 |
⊢ ( ( 𝜑 ↔ 𝜓 ) → ( ( 𝜑 ∨ 𝜒 ) ↔ ( 𝜓 ∨ 𝜒 ) ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
id |
⊢ ( ( 𝜑 ↔ 𝜓 ) → ( 𝜑 ↔ 𝜓 ) ) |
| 2 |
1
|
orbi1d |
⊢ ( ( 𝜑 ↔ 𝜓 ) → ( ( 𝜑 ∨ 𝜒 ) ↔ ( 𝜓 ∨ 𝜒 ) ) ) |